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Noncommutative Geometry and the Physics of the LHC Era

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Quantum Mathematical Physics

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Abstract

Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and general relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the standard model and reduces the number of degrees of freedom. After an introduction of the basic ideas of Noncommutative geometry, I will present its predictions for the standard model and the few known models beyond the standard model based on a classification scheme for finite spectral triples. Most of these models, including the Standard Model, are now ruled out by LHC data. But interesting extensions of the standard model which agree with the presumed Higgs mass, predict new particles (Fermions, Scalars and Bosons) and await further experimental data.

Mathematics Subject Classification (2010). Primary 99Z99; Secondary 00A00

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Acknowledgements

The author wishes to thank the organisers of the conference for the kind invitation and the possibility not only to give a talk but also to enjoy so many splendid talks from colleges and interesting discussions.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Christoph A. Stephan

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  1. Christoph A. Stephan
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Correspondence to Christoph A. Stephan .

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Editors and Affiliations

  1. Universität Regensburg, Fakultät für Mathematik, Regensburg, Germany

    Felix Finster

  2. Regensburg, Germany, Fakultät für Mathematik Universität Rege, Regensburg, Germany

    Johannes Kleiner

  3. Regensburg, Germany, Fakultät für Mathematik Universität Rege, Regensburg, Germany

    Christian Röken

  4. Leipzig, Germany, MPI für Mathematik in den Naturwissensch, Leipzig, Germany

    Jürgen Tolksdorf

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Stephan, C.A. (2016). Noncommutative Geometry and the Physics of the LHC Era. In: Finster, F., Kleiner, J., Röken, C., Tolksdorf, J. (eds) Quantum Mathematical Physics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-26902-3_20

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